docs: def schur_complement(mat, row, col):
      """ compute the schur complement of the matrix block mat[row:,col:] of the matrix mat """
      a = mat[:row, :col]
      b = mat[:row, col:]
      c = mat[row:, :col]
      d = mat[row:, col:]
      return a - b.dot(d.I).dot(c)